Speed of light vertical and horizontal in gravity

[Zman]

The speed of light in a gravitational field is predicted to vary between the horizontal and the vertical.
This prediction comes from the Schwarzschild solution.

The vertical speed c = c_of
The horizontal speed c = c_oSQRT(f)

Where f is 1-2GM/rc²
Because f is smaller than 1, the vertical speed of light is less than the horizontal speed.
Presumably the vertical speed can be down or up which means that it is independent of the direction of gravity as long as it is parallel with the gravity.

Has there been an experiment to test for this prediction?

Is this just an issue of coordinate speed?
It is universally agreed that the speed of light measured locally is independent of direction and always give c.

 

[Ich]

Is this just an issue of coordinate speed?

Yes.
The measurable speed of light is to first order independent of direction even in a gravitational field.

 

[Entropia]

However, in a gravitational field, the speed of light can appear to vary depending on the direction it is measured in. This is known as the "coordinate speed" of light. The Schwarzschild solution predicts that the vertical and horizontal components of the coordinate speed of light will be different, with the vertical speed being slower than the horizontal speed.

There have been numerous experiments conducted to test this prediction, including the Pound-Rebka experiment and the Hafele-Keating experiment. Both of these experiments have confirmed the prediction of the Schwarzschild solution, showing that the speed of light does indeed vary in a gravitational field.

It is important to note that this is not simply an issue of coordinate speed, but rather a fundamental property of space-time in the presence of gravity. The curvature of space-time caused by a massive object, such as a planet or star, affects the path of light and can cause it to appear to travel at different speeds in different directions.

Overall, the prediction of the Schwarzschild solution and the experimental evidence supporting it provide further evidence for the validity of Einstein's theory of general relativity. It also highlights the complex and fascinating nature of gravity and its effects on the behavior of light.